Mark Recapture Background Spring 19 PDF

Preview

Summary

lab notes...

Description

MARK RECAPTURE LAB: ESTIMATING POPULATION SIZE Objectives: Learn common mark-recapture method for estimating population size Learn the assumptions of the mark-recapture technique Describe the conditions that provide the best population estimates using mark-recapture Learn common techniques used for mark-recapture methods

Assignments: Moodle Quiz (5pts) Mark-Recapture Worksheet (10 pts)

Marked individuals of bighorn sheep, the California condor, and salmon. Image credit: Population demography: Fig. 3 by OpenStax College, Biology, CCBY 4.0; originals: left, modification of work by Neal Herbert, NPS; middle, modification of work by Pacific Southwest Region USFWS; right, modification of work by Ingrid Taylar.

1

BACKGROUND POPULATIONS Populations are a group of individuals of the same species at the same place at the same time. Ecology is the study of the environmental factors that influence organismal abundance and distribution. In order to understand what factors influence a population, ecologists must be able to measure the number of individuals in a population. For example, to understand how competition, the -/- interaction between individuals, impacts the interacting populations (intra- or interspecific), you will need to measure changes in population size across competitive interactions in time and space. Understanding changes in population size is also important for Conservation biologists to monitor threatened and endangered species, Disease Ecologists to predict when, if, and where outbreaks are likely to occur or spread. Because of the importance of knowing how large a population is and how it may change across space or time, there are many methods used to measure and estimate population size.

METHODS FOR MEASURING POPULATION SIZE Direct Counts The most direct way to determine how many individuals are in a population is to count all of them. In a few rare cases it is possible to count all individuals in a focal area. For example, large immobile species such as mature trees in a relatively small area (e.g., 1 hectare forest stand). In general, direct counts are possible when organisms are restricted to a finite area (e.g., a small island), are easy to see (e.g., elephants), and are sessile (e.g., barnacles). Direct counts are also commonly attempted for species that are rare or under high conservation concern. However, for most organisms, even those listed about, it is often more feasible to estimate density, the number of individuals per unit area, rather than spending the time and energy counting every single organism. Plot Sampling (area-based counts) One of the most common and efficient ways to estimate population size is by directly counting individuals in a defined area. The number of individuals in a given area or volume are counted in multiple randomly dispersed plots in the area of interest. These counts from multiple equi-sized plots are then used to estimate population size of the whole area of interest by extrapolating the central tendency (average, median, or mode) of individuals from the smaller areas. Typically, the average number of individuals per unit area (or volume) is calculated. This method works well for many kinds of species and habitats, and is particularly well suited for studies of relatively immobile species like plants and small insects. What is a plot? In plot sampling methods, ‘plots’ can be defined in many ways. The key will be to: 1) randomize and replicate samples, and 2) be sure you know what quantity you wish to estimate – do not attempt to extrapolate beyond the bounds of your study area. If you wish to estimate the number of sweet gum trees in northern Louisiana, then you need to randomly sample plots throughout northern Louisiana; sampling plots in one woodland does not allow you to extrapolate outside that woodland. Plots can be defined broadly without much change in the general concept of plot sampling. For example, to estimate the number of sunfish in farm ponds in Ouachita Parish, ‘plots’ might be randomly selected farm ponds within Ouachita Parish. In this case, the study will yield an estimate and confidence interval for the number of sunfish in farm ponds in Ouachita Parish. The fact that the ponds differ in area and are not part of a sample “grid” does not impose problems for interpretation. As with any study, the goal should be specified, and then an appropriate sample protocol can be established to meet the study’s objective. Plot Sampling example: A team of Entomologists (scientists who study insects) want to estimate the population of chinch bugs in a 400ha (ca. 1,000 acre; 1 ha = 10,000m2) field of corn. They count chinch bugs in

2

five 10 cm x 10cm quadrats (i.e., 0.01 m2) and their counts were 40, 10, 70, 80, & 50, they would estimate there was an average of 50 ((40+10+70+80+50) / 5) chinch bugs per 0.01 m2 or 5000 chinch bugs per m2. Thus, in 400 ha there would be an estimated 20 billion chinch bugs (5000 m-2 x 10,000 m2, x 400 ha = 20,000,000,000). This is an estimate of population density. How good is this estimate of population density? We know that the actual population density is not likely to be exactly equal to our estimate because we only sampled a fraction of the entire area. The density estimate might be close to the correct value, or it might be way off. How can we tell? Because we only sample a subset of the total area, we can never know with absolute certainty how good our estimate is, but we can use some statistical methods to quantify the accuracy of our estimate. One good technique for this is to calculate the 95% confidence interval for the density estimate. The confidence interval for an estimate tells us range of values within which the actual density is likely to fall. This concept is easiest to grasp with a specific example. Let’s say that a researcher estimates the density of oak trees in a woodland to be 5.6 per plot, and calculates the 95% confidence interval to be 2.4. The density estimate and confidence interval are typically written as 5.6 ± 2.4. We interpret this to mean that we are 95% confident that the real population density lies between 3.2 (that is, 5.6 minus 2.4) and 8.0 (that is, 5.6 plus 2.4). The confidence interval provides a measure of the reliability of the population density estimate, and is therefore an essential feature of any population study. An estimate of population density is of little use unless it is accompanied by a measure of the reliability of the estimate. We can calculate the 95% confidence interval, CI, as where s is the standard deviation of the samples and n is the number of plots sampled. This equation applies

æ s ö ÷÷ 1.96 ´ çç è nø when the sample size is large. In class, we will use a prepared spreadsheet program to calculate density and its confidence interval, but will use a formula that is applicable to any sample size. CI

Notice that the only parameter of the confidence interval equation that a researcher can control is the sample size, n. The confidence interval decreases as the sample size increases. Thus the reliability of the population estimate increases as more plots are sampled. Unfortunately, however, notice that halving the confidence interval requires quadrupling the sample size because of the square root relationship with sample size. Thus, increased reliability comes at a substantial cost in terms of a researcher’s time and resources. Randomize & replicate! Sample plots should be selected at random and several replicate plots are required. Randomization is the only way to assure unbiased sampling of the habitat, and replication is the only way to evaluate the reliability of the density estimate. Assumptions of Plot Sampling Methods 1. Sample plots are selected at random from the entire region for which the density estimate is meant to apply. 2. All individuals within a sample plot are counted. 3. Individuals do not move between plots during the study. Mark-Recapture Population densities of many animal species are difficult to estimate with the plot sampling technique. For example, birds in a forest may move frequently from one plot to another and may move away from human observers. Also, fish in a lake are difficult to assess by plot sampling because they are highly mobile and difficult to observe without substantial disturbance that may cause them to leave a plot. For these and many other mobile species, a set of population density estimation methods called “mark-recapture” methods are more appropriate. In general, the mark-recapture method relies on capturing individuals in the initial sample, marking these individuals, then sampling the population again and counting the number of individuals in the second 3

sampling that were recaptured. There are many kinds of mark-recapture methods, each tailored to meet different goals of a research project or special challenges posed by different species. We will focus on two very general methods: the Peterson method and the Schnabel method.

TYPES OF MARK-RECAPTURE METHODS Peterson method The Peterson method is the most simple mark-recapture method. It involves a three step capture-markrecapture process, and provides an intuitively simple and often very accurate estimate of population size. The basic process for the Peterson method is as follows: 1. Collect individuals within the study area (first sample). 2. Mark all the collected individuals in some way, then release them back into the study area where they mix with the general population. 3. Collect individuals in the study area at a later time (second sample). The total population size can then be estimated by solving the proportionality equation: M1/N = R/M2 Where M1 = original number of sampled and marked individuals at Time 1 sampling, N= total population size, R= recaptured individuals, M2 = the number of individuals sampled at the Time 2 sampling period. The only unknown in this equation is the total population size (N), so we can rearrange the equation and solve for N to estimate the total population size: N = (M1 x M2)/R For example: You capture 23 butterflies from a meadow in your first sampling. You mark these individuals then release them (M1). A day later, you sample the meadow again, and capture 15 individuals (M2), 4 of these are marked (R); Thus, we can estimate total population size as: (23 x 15) / 4 = 86 butterflies in the meadow. As always, this estimated value of the population size is of little use unless we also have an estimate of its reliability. Statisticians have devised a method to approximate the 95% confidence interval for the Peterson method, which is given by: CI = 1.96 √

𝑀12 (𝑀2 + 1)(𝑀2 – R) (R + 1)2 (R + 2)

Thus, if our population estimate is 86, and our 95% confidence interval is 73, then we would write, N = 86 ± 25 and we interpret this result to mean that our best estimate of the real population size is 86, and we are 95% confident that the real population size lies between 61 (that is, 86 minus 25) and 111 (that is, 86 plus 25). Schnabel method The Schnabel method works on the same principle as the Peterson method, but is a generally more accurate method of estimating population size than the Peterson method. As you might expect, this greater accuracy comes at the cost of greater time and effort in sampling the population. The Schnabel method gains its greater 4

accuracy by repeatedly sampling and marking individuals over time. Instead of collecting only one recapture sample, as in the Peterson method, the Schnabel method uses multiple recapture samples, providing a more accurate and reliable estimate of population density. This method is especially useful in studies of animals that are difficult to capture and can only be sampled in small numbers. For animals with these characteristics, snakes, for example, the Peterson method would provide a very unreliable population estimate, and the Schnabel method is recommended. The Schnabel procedure works as follows. The researcher obtains an initial sample, and all individuals are marked and released. Some time later a second sample is collected, the total number of individuals and the number of marked individuals are recorded, and all unmarked individuals in the sample are marked and released. The researcher continues to collect samples in this way until a suitable level of reliability is reached or until a predetermined number of samples are obtained. Calculations for the Schnabel method are more complicated, and we will simply use a spreadsheet program to analyze data. A detailed description of the Schnabel method and other mark-recapture methods is presented in the book Ecological Methodology by Charles J. Krebs. Here is the formula: 𝑁=

∑𝑆𝑡=1 (𝐶𝑡 𝑀𝑡 ) (∑𝑆𝑡=1 𝑅𝑡 )

Where S is the number of sample events, Ct is the # captured at tth sample event, Mt is the total # of marked individuals in the population during the tth sample event, and, Rt is the # of individuals recaptured during the tth sample event

ASSUMPTIONS OF MARK-RECAPTURE METHODS Mark-recapture methods are based on several assumptions: 1. The population size is large. If the population size is not large then capture rates are likely low in general and estimates will be inaccurate (typically too high). 2. The population size remains constant during the study period (e.g., There is no immigration, emigration, births or deaths between samples) If marked individuals die and are replaced with newborns, you will recapture few or no marked individuals and estimates will be too high. This not a large concern for organisms with only one reproductive period per year like box turtles, but can significantly affect estimates for rapidly breeding organisms. If individuals leave the area and new once come in and replace them, you will get fewer recaptures than the equilibrium pop size. 3. The probability of capturing a marked animal is the same as that of capturing any member of the population. If marking an animal stresses it or frightens it causing it to hide and avoid capture more than those without marks, then recaptures will be underreprented in a second sample. On the other hand, if the individual becomes more tame and easier to recapture, then the opposite error is introduced. 4. Marks are not lost between samples and do not affect the survival of the marked organism. Invertebrates molt and shed skins with marks, mammals can wriggle out of collars, or environmental factors may cause marks to be obscured. If this happens than recaptures will be undercounted and your estimate will be too high. If marking individuals causes the individual to have increased mortality (e.g., through stress, increased risk of predation, etc.) then recaptures will be lower and estimates of pop size too high.

5

Violation of one or more assumptions will cause the estimated population size to be biased. In practice, small violations can often be ignored. In some cases it will be possible to determine the degree to which the estimate is biased, and then correct the estimate accordingly. For example, there are mathematical methods to test whether the assumption of equal catchability was violated. There are also more complicated mark-recapture models that allow for and attempt to estimate immigration and emigration (termed open population models). The more simple models we are working with today are classified as closed population models. Objectives In this lab, you will learn to use various methods to estimate population size and compare and contrast these methods in terms of efficacy and efficiency. Exercise You will use the various methods to estimate the population size of mobile nano bugs and sessile flowers. There will be 5 stations: 2 Direct counting, 2 plot sampling, 1 Peterson mark-recapture that is combined with the Schnabel mark-recapture. You will work in 5 groups of 4 people.

6

Part 1: Determining Population Size with the Various Methods Below you will find the directions for each of the 6 stations for measuring population size. Each person in a group should complete their own worksheet. Station 1: Direct Counting of Sessile Organisms (1) Record start time in minutes and seconds. (2) Each person should individually count all the flowers and record the number on the data sheet. (3) Record finish time in minutes and seconds. (4) Wait to rotate to the next station. Station 2: Direct Counting of Mobile Organisms (1) Record start time in minutes and seconds. (2) Each person should individually count all the moving nano bugs and record the number on the data sheet. (3) Record finish time in minutes and seconds. (4) Wait to rotate to the next station. Station 3: Plot Sampling Sessile Organisms (1) Randomly distribute your flowers across the surface of the gridded box. (2) Record start time in minutes and seconds. (3) Each person should randomly choose 10 plots (e.g., grid boxes) and count the number of flowers in each plot. (4) Record data on data sheet. (5) Record finish time in minutes and seconds. (6) Wait to rotate to the next station. Station 4: Plot Sampling Mobile Organisms (1) Record start time in minutes and seconds. (2) Each person should randomly choose 10 plots (e.g., grid boxes) and count the number of nano bugs in each plot. (3) Record data on data sheet. (4) Record finish time in minutes and seconds. (5) Wait to rotate to the next station.

7

Station 5 Part A: Peterson Mark Recapture Instructions: (1) Choose one member of your group to be the ‘capturer’ and blindfold the person. (2) Set a timer for 10 seconds and make sure all nano bugs are moving. (3) Start timer and have blindfolded person ‘capture’ as many nano bugs as possible by grabbing them and putting them in a bucket. YOU MAY ONLY GRAB ONE BUG IN ONE HAND AT A TIME. Place that bug in the bucket before grabbing the next. No sweeping your hands across the box to collect multiple bugs at the same time. (4) At the end of the time, have the group count and record the number of individual nano bugs collected. (5) Mark each of the collected nano bug individuals with a sticker (6) Redistribute marked nano bugs into the box. (7) Re-blindfold the same person and set the time for another 10 seconds. (8) Start the timer and have the blindfolded person take a second sample placing collected nano bugs into the bucket (set this sample aside, we will use it again for the Schnable Mark-Recapture Method). (9) Count and record the number of collected marked and unmarked nano bug individuals on data sheet. (10) Continue with the blindfolded person to the Schnable mark-recapture methods below before switching group members. Station 5 Part B: Schnabel Mark-Recapture Instructions (1) Use the 1st capture from the Peterson method as your first sample for Schnabel. (2) Using the 2nd sample from the Peterson method that you set aside earlier, record the total number of nano bugs in your sample (Mi) and the number of those that were recaptures (previously marked (Ri)). (3) Mark all of the unmarked nano bugs in your second sample and redistribute marked nano bugs in the box. (4) Re-blindfold the same person and set the time for another 10 seconds. (5) Start the timer and have the blindfolded person take a third sample placing collected nano bugs into the bucket. (6) After the 10 s are done, count the number of marked and unmarked nano bugs in the third collection. (7) Record the total number of nanobugs in your sample (Mi) and the number of those that were recaptures (mi) (8) Repeat above instructions 3-5 until you have at least 6 capture cycles. (9) Record data on data sheet.

After everyone has rotated through all stations, turn off nano bugs, and directly count the actual abundance of both the sessile (daisies) and mobile (nanobugs) at each station. Record this on your data sheets.

8

Data Sheet

Name: ___________________

Station 1: Direct Counting of Sessile Organisms Time Start (Ts)

Number of Flowers

Time Finish (Tf)

Total Time (Tf-Ts)

Time Finish (Tf)

Total Time (Tf-Ts)

Station 2: Direct Counting of Mobile Organisms Time Start (Ts)

Number of nano ...